Got hold of a very poorly Rainbow Islands Extra board.
This board had some repair work done previously. There are a few burned out tracks and some dodgy looking wire links.

On power up it just showed a black screen, time to break out the Fluke 9010a.
The Fluke showed I had active interrupt lines. The 68000 CPU has 3 interrupts, IPL0, IPL1 and IPL2. IPL1 and 2 are tied to +5v (they are active low therefore unused here). IPL2 was stuck low.
I traced the line to a nearby 74ALS74 chip and then back to a 74LS273 (IC32). Regardless what the inputs were doing, the outputs were all stuck low. I replaced this and tested, still a blank screen. I check the 74ALS74 again and although all the inputs were now present and correct, its output to IPL2 was still stuck low. I piggybacked a new IC onto it and the game came to life. Replaced the IC.

Now the game booted up I could see that the colours of the character sprites were wrong, mainly black.

This caused me a lot of headache as the colours came good when I put the logic probe on different pins of different IC’s. I determined which IC was partially responsible for sprite colours by interrupting lines on various logic chips. I found that if I toggled pin 9 of IC35 (74LS157) the colours came good more regular. I removed this chip and tested it in my logic tester, it passed but if I put it on a loop it would intermittently fail. Replaced this and the colours were now back to normal.

There is also a problem when the sprites are facing left where it shows a broken character but still facing right. The pictures below shows the broken up boss sprite and broken rainbows when fired to the left.

This ended up being a short on pin 15 @ IC38 (74LS153). This pin was shorted very slightly to an exposed track running next to it. Removing this short fixed the graphics completely and the game is now 100%.
Very pleased.